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2 years ago

6

lemma wants to build a road named stargazer boulevard that will be parallel to moonbeam drive, on this road she will build a din

er located 7 blocks north of the community garden where is the diner located

1 answer:

Reil [10]2 years ago

4 0

Answer:

(20,

Step-by-step explanation:

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Estimate each product 5/7×1/9=

Cerrena [4.2K]

Multiply it out to get 5/7*1/9=5/63. This is an exact value of the product.

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2 years ago

Two buses leave towns 1631km apart at the same time and travel toward each other. one bus travels 17 /kmh slower than the other.

Blababa [14]

Suppose one bus travels at x km/h, the second bus is 17 km/h slower so it is x-17
the first bus travels a total of 7x km, the second bus travels 7(x-17)km, together they travel the total distance of 1631 km
7x + 7(x-17) =1631
7x + 7x -119 =1631
14x=1750

x=125
x-17=108

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3 years ago

Prove by mathematical induction that

postnew [5]

For $n=1$ , on the left we have $\cos\theta$ , and on the right,

$\dfrac{\sin2\theta}{2\sin\theta}=\dfrac{2\sin\theta\cos\theta}{2\sin\theta}=\cos\theta$

(where we use the double angle identity: $\sin2\theta=2\sin\theta\cos\theta$ )

Suppose the relation holds for $n=k$ :

$\displaystyle\sum_{n=1}^k\cos(2n-1)\theta=\dfrac{\sin2k\theta}{2\sin\theta}$

Then for $n=k+1$ , the left side is

$\displaystyle\sum_{n=1}^{k+1}\cos(2n-1)\theta=\sum_{n=1}^k\cos(2n-1)\theta+\cos(2k+1)\theta=\dfrac{\sin2k\theta}{2\sin\theta}+\cos(2k+1)\theta$

So we want to show that

$\dfrac{\sin2k\theta}{2\sin\theta}+\cos(2k+1)\theta=\dfrac{\sin(2k+2)\theta}{2\sin\theta}$

On the left side, we can combine the fractions:

$\dfrac{\sin2k\theta+2\sin\theta\cos(2k+1)\theta}{2\sin\theta}$

Recall that

$\cos(x+y)=\cos x\cos y-\sin x\sin y$

so that we can write

$\dfrac{\sin2k\theta+2\sin\theta(\cos2k\theta\cos\theta-\sin2k\theta\sin\theta)}{2\sin\theta}$

$=\dfrac{\sin2k\theta+\sin2\theta\cos2k\theta-2\sin2k\theta\sin^2\theta}{2\sin\theta}$

$=\dfrac{\sin2k\theta(1-2\sin^2\theta)+\sin2\theta\cos2k\theta}{2\sin\theta}$

$=\dfrac{\sin2k\theta\cos2\theta+\sin2\theta\cos2k\theta}{2\sin\theta}$

(another double angle identity: $\cos2\theta=\cos^2\theta-\sin^2\theta=1-2\sin^2\theta$ )

Then recall that

$\sin(x+y)=\sin x\cos y+\sin y\cos x$

which lets us consolidate the numerator to get what we wanted:

$=\dfrac{\sin(2k+2)\theta}{2\sin\theta}$

and the identity is established.

8 0

2 years ago

A package of 3 pairs of insulated costs $23.67. What is the unit price of the pairs of gloves ?

amm1812

The unit price is $7.89
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2 years ago

Solve for x. Answer in Interval Notation using Grouping Symbols.<br> x^2+9x<36

4vir4ik [10]

Answer:

$-12$

In interval notation: (-12,3)

Step-by-step explanation:

To solve the expression shown in the problem you must:

- Subtract 36 from both sides, then:

$x^{2}+9x-36$

- Now you must find two number whose sum is 9 and whose produt is 36. These would be -3 and 12. Then, you have:

$(x-3)(x+12)$

- Therefore the result is:

$-12$

In interval notation:

(-12,3)

5 0

2 years ago

Read 2 more answers